Trying to hang the self-made gymnastics workout machine in the garage

I basically made this machine referencing two videos:

1. Power Moves Training System
2. How to Make Your Own Breakdancing Flare Trainer

Mine is a tiny bit different than both but same basic design. It's basically as compact as the first one but uses simple items like the second one.

I had also built a 10ft long, 8ft wide, and 10ft tall structure that contains several workout items that I can swap out with carabiner clips attached to eyehooks.

The problem is in this system my legs swing across the whole structure and the crossbeams I placed for support get in the way as they are only 4ft (and some inches) away from me on either side. I should've made the whole structure 10x10x10 so that issue wouldn't exist but I wasn't thinking obviously.

So now I am trying to hang the machine from a joist in the top.

There are two problems:

1) It is stucco and I am unsure if something like this will eventually crack it over time due to movement. If that is the case I have no clue how to prevent such damage.

I've seen solutions such as this and this but have no clue how either were accomplished without damaging the stucco or making sure the movement wont damage it overtime.

2) The garage is directly under a room and I have no idea how I would get on the other side of the joist in order to secure it with a nut.

The only easy solution I see is an exposed beam that is still stucco covered but I could put the eye hook horizontally and place the nut after drilling it through the other side. However there is one problem with that as well. There is a garage opening mechanism close to it and I'm afraid that when I use this flare machine it will hit it pretty often if not every time. Thus why I'd prefer using a joist.